2020/12/13 by Artur Kawalec, Kawalec, Artur
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2012.06581
openalex publication_date 2020/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we develop four types of analytical recurrence formulas for\nnon-trivial zeros of the Riemann zeta function on critical line assuming (RH).\nThus, all non-trivial zeros up to the nth order must be known in order to\ngenerate the nth+1 non-trivial zero. All the presented formulas are based on\ncertain closed-form representations of the secondary zeta function family,\nwhich are already available in the literature. We also present a formula to\ngenerate the non-trivial zeros directly from primes. Thus all primes can be\nconverted into an individual non-trivial zero, and we also give a set of\nformulas to convert all non-trivial zeros into an individual prime. We also\nextend the presented results to other Dirichlet-L functions, and in particular,\nwe develop an analytical recurrence formula for non-trivial zeros of the\nDirichlet beta function. Throughout this article, we also numerically compute\nthese formulas to high precision for various test cases and review the computed\nresults.\n